Sobolev regularity of bivariate isogeometric finite element spaces in case of a geometry map with degenerate corner Sobolev regularity of bivariate isogeometric finite element spaces

We investigate Sobolev regularity of bivariate functions obtained in Isogeometric Analysis when using geometry maps that are degenerate in the sense that the first partial derivatives vanish at isolated points. In particular, we show how the known C 1 -conditions for D-patches have to be tightened t...

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Bibliographic Details
Published inAdvances in computational mathematics Vol. 50; no. 6
Main Author Reif, Ulrich
Format Journal Article
LanguageEnglish
Published New York Springer US 01.12.2024
Subjects
Computational Mathematics and Numerical Analysis
Computational Science and Engineering
Mathematical and Computational Biology
Mathematical Modeling and Industrial Mathematics
Mathematics
Mathematics and Statistics
Visualization
Isogeometric analysis
Degenerate parametrization
Sobolev regularity
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Summary:We investigate Sobolev regularity of bivariate functions obtained in Isogeometric Analysis when using geometry maps that are degenerate in the sense that the first partial derivatives vanish at isolated points. In particular, we show how the known C 1 -conditions for D-patches have to be tightened to guarantee square integrability of second partial derivatives, as required when computing finite element approximations of elliptic fourth order PDEs like the biharmonic equation.
ISSN:1019-7168
1572-9044
DOI:10.1007/s10444-024-10203-x